The fumes are not what is toxic. What is toxic is the phenol resins that exist within softwoods, which do NOT exist in high concentration - if they even exist at all - in the bark, only in the wood itself. Even pine shavings can be used if they don't have a strong smell - the smell is merely an indication of the phenol resins present.

If you're going to use a bark mulch though, use Cypress. Better safe than sorry.